If 35.7 kPa of Bromine gas takes up 41.3 L, how much volume will the gas take up at 13.8 kPa

This follows Boyles law which relates pressure and volume. The law states that pressure is inversely proportional to volume at a constant temperature.

PV = k

where k is a constant.

At two instances;

P1V1 = P2V2

where parameters for the 1st instance is on the left and parameters for the second instance is on the right.

37.5 kPa x 41.3 L = 13.8 kPa x V2

V2 = 37.5 x 41.3 / 13.8

V2 = 112.23 L

At the new pressure gas will take up a volume of 112.23 L